def setUp(self):
gs.random.seed(1234)
self.n = 3
self.n_samples = 2
self.group = GeneralLinearGroup(n=self.n)
# We generate invertible matrices using so3_group
self.so3_group = SpecialOrthogonalGroup(n=self.n)
warnings.simplefilter('ignore', category=ImportWarning)
def __init__(self, n):
assert isinstance(n, int) and n > 0
super(SPDMatricesSpace,
self).__init__(dimension=int(n * (n + 1) / 2),
embedding_manifold=GeneralLinearGroup(n=n))
self.n = n
self.metric = SPDMetric(n=n)
def __init__(self, n):
assert isinstance(n, int) and n > 1
self.n = n
self.dimension = int((n * (n - 1)) / 2)
LieGroup.__init__(self,
dimension=self.dimension,
identity=gs.zeros(self.dimension))
EmbeddedManifold.__init__(self,
dimension=self.dimension,
embedding_manifold=GeneralLinearGroup(n=n))
self.bi_invariant_metric = self.left_canonical_metric
self.point_representation = 'vector' if n == 3 else 'matrix'
def __init__(self, n, point_type=None):
assert isinstance(n, int) and n > 1
self.n = n
self.dimension = int((n * (n - 1)) / 2)
self.default_point_type = point_type
if point_type is None:
self.default_point_type = 'vector' if n == 3 else 'matrix'
LieGroup.__init__(self, dimension=self.dimension)
EmbeddedManifold.__init__(self,
dimension=self.dimension,
embedding_manifold=GeneralLinearGroup(n=n))
self.bi_invariant_metric = self.left_canonical_metric
class TestGeneralLinearGroupMethods(geomstats.tests.TestCase):
_multiprocess_can_split_ = True
def setUp(self):
gs.random.seed(1234)
self.n = 3
self.n_samples = 2
self.group = GeneralLinearGroup(n=self.n)
# We generate invertible matrices using so3_group
self.so3_group = SpecialOrthogonalGroup(n=self.n)
warnings.simplefilter('ignore', category=ImportWarning)
@geomstats.tests.np_only
def test_belongs(self):
"""
A rotation matrix belongs to the matrix Lie group
of invertible matrices.
"""
rot_vec = gs.array([0.2, -0.1, 0.1])
rot_mat = self.so3_group.matrix_from_rotation_vector(rot_vec)
result = self.group.belongs(rot_mat)
expected = gs.array([True])
self.assertAllClose(result, expected)
def test_compose(self):
# 1. Composition by identity, on the right
# Expect the original transformation
rot_vec = gs.array([0.2, -0.1, 0.1])
mat = self.so3_group.matrix_from_rotation_vector(rot_vec)
result = self.group.compose(mat, self.group.identity)
expected = mat
expected = helper.to_matrix(mat)
self.assertAllClose(result, expected)
# 2. Composition by identity, on the left
# Expect the original transformation
rot_vec = gs.array([0.2, 0.1, -0.1])
mat = self.so3_group.matrix_from_rotation_vector(rot_vec)
result = self.group.compose(self.group.identity, mat)
expected = mat
self.assertAllClose(result, expected)
def test_inverse(self):
mat = gs.array([[1., 2., 3.], [4., 5., 6.], [7., 8., 10.]])
result = self.group.inverse(mat)
expected = 1. / 3. * gs.array([[-2., -4., 3.], [-2., 11., -6.],
[3., -6., 3.]])
expected = helper.to_matrix(expected)
self.assertAllClose(result, expected)
def test_compose_and_inverse(self):
# 1. Compose transformation by its inverse on the right
# Expect the group identity
rot_vec = gs.array([0.2, 0.1, 0.1])
mat = self.so3_group.matrix_from_rotation_vector(rot_vec)
inv_mat = self.group.inverse(mat)
result = self.group.compose(mat, inv_mat)
expected = self.group.identity
expected = helper.to_matrix(expected)
self.assertAllClose(result, expected)
# 2. Compose transformation by its inverse on the left
# Expect the group identity
rot_vec = gs.array([0.7, 0.1, 0.1])
mat = self.so3_group.matrix_from_rotation_vector(rot_vec)
inv_mat = self.group.inverse(mat)
result = self.group.compose(inv_mat, mat)
expected = self.group.identity
expected = helper.to_matrix(expected)
self.assertAllClose(result, expected)
@geomstats.tests.np_and_tf_only
def test_group_log_and_exp(self):
point = 5 * gs.eye(self.n)
group_log = self.group.group_log(point)
result = self.group.group_exp(group_log)
expected = point
expected = helper.to_matrix(expected)
self.assertAllClose(result, expected)
@geomstats.tests.np_and_tf_only
def test_group_exp_vectorization(self):
point = gs.array([[[2., 0., 0.], [0., 3., 0.], [0., 0., 4.]],
[[1., 0., 0.], [0., 5., 0.], [0., 0., 6.]]])
expected = gs.array([[[7.38905609, 0., 0.], [0., 20.0855369, 0.],
[0., 0., 54.5981500]],
[[2.718281828, 0., 0.], [0., 148.413159, 0.],
[0., 0., 403.42879349]]])
result = self.group.group_exp(point)
self.assertAllClose(result, expected, rtol=1e-3)
@geomstats.tests.np_and_tf_only
def test_group_log_vectorization(self):
point = gs.array([[[2., 0., 0.], [0., 3., 0.], [0., 0., 4.]],
[[1., 0., 0.], [0., 5., 0.], [0., 0., 6.]]])
expected = gs.array([[[0.693147180, 0., 0.], [0., 1.09861228866, 0.],
[0., 0., 1.38629436]],
[[0., 0., 0.], [0., 1.609437912, 0.],
[0., 0., 1.79175946]]])
result = self.group.group_log(point)
self.assertAllClose(result, expected, atol=1e-4)
@geomstats.tests.np_and_tf_only
def test_expm_and_logm_vectorization_symmetric(self):
point = gs.array([[[2., 0., 0.], [0., 3., 0.], [0., 0., 4.]],
[[1., 0., 0.], [0., 5., 0.], [0., 0., 6.]]])
result = self.group.group_exp(self.group.group_log(point))
expected = point
self.assertAllClose(result, expected)
def setUp(self):
gs.random.seed(1234)
n = 3
self.group = GeneralLinearGroup(n=n)
# We generate invertible matrices using so3_group
self.so3_group = SpecialOrthogonalGroup(n=n)
class TestGeneralLinearGroupMethods(unittest.TestCase):
_multiprocess_can_split_ = True
def setUp(self):
gs.random.seed(1234)
n = 3
self.group = GeneralLinearGroup(n=n)
# We generate invertible matrices using so3_group
self.so3_group = SpecialOrthogonalGroup(n=n)
def test_belongs(self):
"""
A rotation matrix belongs to the matrix Lie group
of invertible matrices.
"""
rot_vec = self.so3_group.random_uniform()
rot_mat = self.so3_group.matrix_from_rotation_vector(rot_vec)
self.assertTrue(self.group.belongs(rot_mat))
def test_compose(self):
# 1. Composition by identity, on the right
# Expect the original transformation
rot_vec_1 = self.so3_group.random_uniform()
mat_1 = self.so3_group.matrix_from_rotation_vector(rot_vec_1)
result_1 = self.group.compose(mat_1, self.group.identity)
expected_1 = mat_1
self.assertTrue(gs.allclose(result_1, expected_1))
# 2. Composition by identity, on the left
# Expect the original transformation
rot_vec_2 = self.so3_group.random_uniform()
mat_2 = self.so3_group.matrix_from_rotation_vector(rot_vec_2)
result_2 = self.group.compose(self.group.identity, mat_2)
expected_2 = mat_2
norm = gs.linalg.norm(expected_2)
atol = RTOL
if norm != 0:
atol = RTOL * norm
self.assertTrue(
gs.allclose(result_2, expected_2, atol=atol), '\nresult:\n{}'
'\nexpected:\n{}'.format(result_2, expected_2))
def test_compose_and_inverse(self):
# 1. Compose transformation by its inverse on the right
# Expect the group identity
rot_vec_1 = self.so3_group.random_uniform()
mat_1 = self.so3_group.matrix_from_rotation_vector(rot_vec_1)
inv_mat_1 = self.group.inverse(mat_1)
result_1 = self.group.compose(mat_1, inv_mat_1)
expected_1 = self.group.identity
norm = gs.linalg.norm(expected_1)
atol = RTOL
if norm != 0:
atol = RTOL * norm
self.assertTrue(
gs.allclose(result_1, expected_1, atol=atol), '\nresult:\n{}'
'\nexpected:\n{}'.format(result_1, expected_1))
# 2. Compose transformation by its inverse on the left
# Expect the group identity
rot_vec_2 = self.so3_group.random_uniform()
mat_2 = self.so3_group.matrix_from_rotation_vector(rot_vec_2)
inv_mat_2 = self.group.inverse(mat_2)
result_2 = self.group.compose(inv_mat_2, mat_2)
expected_2 = self.group.identity
norm = gs.linalg.norm(expected_2)
atol = RTOL
if norm != 0:
atol = RTOL * norm
self.assertTrue(gs.allclose(result_2, expected_2, atol=atol))
class TestGeneralLinearGroupTensorFlow(tf.test.TestCase):
_multiprocess_can_split_ = True
def setUp(self):
gs.random.seed(1234)
n = 3
self.group = GeneralLinearGroup(n=n)
# We generate invertible matrices using so3_group
self.so3_group = SpecialOrthogonalGroup(n=n)
@classmethod
def setUpClass(cls):
os.environ['GEOMSTATS_BACKEND'] = 'tensorflow'
importlib.reload(gs)
@classmethod
def tearDownClass(cls):
os.environ['GEOMSTATS_BACKEND'] = 'numpy'
importlib.reload(gs)
def test_belongs(self):
"""
A rotation matrix belongs to the matrix Lie group
of invertible matrices.
"""
rot_vec = tf.convert_to_tensor([0.2, -0.1, 0.1])
rot_mat = self.so3_group.matrix_from_rotation_vector(rot_vec)
result = self.group.belongs(rot_mat)
expected = tf.convert_to_tensor([True])
with self.test_session():
self.assertAllClose(gs.eval(result), gs.eval(expected))
def test_compose(self):
# 1. Composition by identity, on the right
# Expect the original transformation
rot_vec = tf.convert_to_tensor([0.2, -0.1, 0.1])
mat = self.so3_group.matrix_from_rotation_vector(rot_vec)
result = self.group.compose(mat, self.group.identity)
expected = mat
expected = helper.to_matrix(mat)
with self.test_session():
self.assertAllClose(gs.eval(result), gs.eval(expected))
# 2. Composition by identity, on the left
# Expect the original transformation
rot_vec = tf.convert_to_tensor([0.2, 0.1, -0.1])
mat = self.so3_group.matrix_from_rotation_vector(rot_vec)
result = self.group.compose(self.group.identity, mat)
expected = mat
with self.test_session():
self.assertAllClose(gs.eval(result), gs.eval(expected))
def test_inverse(self):
mat = tf.convert_to_tensor([[1., 2., 3.], [4., 5., 6.], [7., 8., 10.]])
result = self.group.inverse(mat)
expected = 1. / 3. * tf.convert_to_tensor(
[[-2., -4., 3.], [-2., 11., -6.], [3., -6., 3.]])
expected = helper.to_matrix(expected)
with self.test_session():
self.assertAllClose(gs.eval(result), gs.eval(expected))
def test_compose_and_inverse(self):
# 1. Compose transformation by its inverse on the right
# Expect the group identity
rot_vec = tf.convert_to_tensor([0.2, 0.1, 0.1])
mat = self.so3_group.matrix_from_rotation_vector(rot_vec)
inv_mat = self.group.inverse(mat)
result = self.group.compose(mat, inv_mat)
expected = self.group.identity
expected = helper.to_matrix(expected)
with self.test_session():
self.assertAllClose(gs.eval(result), gs.eval(expected))
# 2. Compose transformation by its inverse on the left
# Expect the group identity
rot_vec = tf.convert_to_tensor([0.7, 0.1, 0.1])
mat = self.so3_group.matrix_from_rotation_vector(rot_vec)
inv_mat = self.group.inverse(mat)
result = self.group.compose(inv_mat, mat)
expected = self.group.identity
expected = helper.to_matrix(expected)
with self.test_session():
self.assertAllClose(gs.eval(result), gs.eval(expected))